Evaluation of biodynamic models from walking tests for civil engineering applications

Abstract

Structural vibrations induced by human activities, such as walking, have become a significant concern from a design perspective, especially due to modern structures featuring low natural frequencies. A key aspect of this field in dynamics is the Human-Structure Interaction (HSI) phenomenon, which refers to the feedback loop between occupants and pedestrian structures, such as footbridges and floors. In this context, human walking models designed to simulate HSI have gained interest for civil engineering applications. Focusing on walking in the vertical direction, so-called biodynamic models have been introduced to represent pedestrians, with approaches ranging from mathematical assumptions to kinematic representations of the body. Among the simplest biodynamic models, two approaches stand out in HSI investigations: the single-degree-of-freedom (SDOF) spring-mass-damper (SMD) model and the damped bipedal inverted pendulum (DBIP) model. While the SMD model approximates the ground reaction force (GRF) transmitted to the structure as a coupled moving force acting at a single contact point, the DBIP model calculates GRFs based on selected parameters and the model’s motion, transmitting them to the ground while accounting for the relative position of both feet during walking. Despite both models being capable of reproducing interaction forces, DBIP models, unlike SMD models, have the potential to capture changes in walking patterns due to surface vibrations. This is because, in DBIP models, the step frequency is not an input parameter but rather a consequence of the model’s motion. In this context, this study aimed to evaluate both models for civil engineering applications based on walking tests. The performance of SMD and DBIP models was initially analysed by applying an HSI formulation using experimental structural acceleration time-history data from two lively footbridges. While SMD models performed well, DBIP models tended to overestimate the structural response due to the high values of dynamic load factors (DLFs) produced, even while accurately reproducing the walking speed and step frequency pairs. Further investigations of DBIP models were conducted using kinetic and kinematic data from experimental walking tests performed on a moving platform equipped with force plates. In rigid surface scenarios, results from three test subjects confirmed that DBIP models tend to overestimate DLFs while simultaneously reproducing experimental walking speeds and step frequencies. However, these models could qualitatively predict trends in variations of applied forces due to surface vibrations – something not possible with SMD models, as their GRFs are predefined inputs. Additionally, experimental insights from moving surface scenarios highlighted that significant changes in applied forces can occur, depending on the surface’s vertical displacement levels and its vertical position at the moment of foot contact – factors neglected by existing guidelines and standards adopted for the design of structures.